I stumbled over #262 http://trac.sagemath.org/sage_trac/ticket/262
again. Here Graeme Taylor proposes his implementation of point counting of elliptic curves over GF(p^n) with coefficients in GF(p) in Weierstrass form. He describes the background at: http://maths.straylight.co.uk/archives/69 . This was turned down because a patch by Alex Ghitza http://www.sagemath.org/hg/sage-main/rev/57bc9076e61a implements the same functionality. I can see that this implements the same functionality but I find the interface rather complicated: The user is required to construct the curve over the prime subfield and ask for the cardinality over a higher degree extension via an optional parameter 'degree'. E.g. sage: k.<a> = GF(7^10) sage: E = EllipticCurve(k,[5,2]) sage: E2 = EllipticCurve(k.base_ring(), E.a_invariants()) # down sage: E2.cardinality(10) # and up again 282464343 I wonder why not just compute the cardinality using this method by default if all coefficients lie in the prime subfield? Is this optional 'degree' parameter really necessary? Just curious, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
